Question

Racionalize $\frac{sqrt(2)-1}{2-sqrt(2)}$

Answer 1

]Multiplique o termo pelo seu conjugado
no caso:2+ \sqrt{2} / 2+\sqrt{2}

Answer 2

$\frac{ \sqrt{2} -1}{2- \sqrt{2} } = \\ \\ \frac{( \sqrt{2}-1)(2+ \sqrt{2} ) }{(2- \sqrt{2})(2+ \sqrt{2} ) } = \\ \\ \frac{2 \sqrt{2}+ \sqrt{4} -2- \sqrt{2} }{4-\not2 \sqrt{2} +\not2 \sqrt{2}- \sqrt{4} } = \\ \\ \frac{2 \sqrt{2}- \sqrt{2} +\not2-\not2 }{4-2} = \\ \\ \frac{ \sqrt{2} }{2}$